2024/10/10 by Jesús Palma-Márquez, Palma-Márquez, Jesús, Melvin Yeung +1
Engineering · Computer Science · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Advanced Mathematical Modeling in Engineering #Heat Transfer and Mathematical Modeling
paper · pdf · doi:10.48550/arxiv.2410.07532
We study large classes of real-valued analytic functions that naturally emerge in the understanding of Dulac's problem, which addresses the finiteness of limit cycles in planar differential equations. Building on a Maximum Modulus-type result we got, our main statement essentially follows. Namely, for any function belonging to these classes, the following dichotomy holds: either it has isolated zeros or it coincides with the identity. As an application, we prove that the non-accumulation of limit cycles holds around a specific class of the so-called superreal polycycles.